Find the LCM and HCF of 24, 15 and 36 Using Prime Factorization

Video Explanation

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Solution

Question: Find the LCM and HCF of the integers 24, 15 and 36 by applying the prime factorization method.

Step 1: Prime Factorization of the Given Integers

24 = 2 × 2 × 2 × 3 = 2³ × 3

15 = 3 × 5

36 = 2 × 2 × 3 × 3 = 2² × 3²

Step 2: Find the HCF

Common prime factor in all three numbers = 3

∴ HCF (24, 15, 36) = 3

Step 3: Find the LCM

LCM is the product of the highest powers of all prime factors:

LCM = 2³ × 3² × 5

LCM = 360

Final Answer

HCF of 24, 15 and 36 = 3
LCM of 24, 15 and 36 = 360

Conclusion

Thus, by using the prime factorization method, we find that the HCF of 24, 15 and 36 is 3 and their LCM is 360.